| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 3.3.6.18a1.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x + 3\right) ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$18$ |
not computed |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 3 t\right) x + 3 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + 1$ |
undefined |
| 3.3.6.18a1.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$6$ |
$18$ |
not computed |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + 1$ |
$[1, 4]$ |
| 3.3.6.18a2.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 3\right) ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$18$ |
not computed |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x + 3 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + t$ |
undefined |
| 3.3.6.18a2.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$6$ |
$18$ |
not computed |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + t$ |
$[1, 4]$ |
| 3.3.6.18a3.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 6 x + 3\right) ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$18$ |
$C_3^2\wr C_3:D_4$ (as 18T599) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 6 t\right) x + 3 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + (t + 2)$ |
undefined |
| 3.3.6.18a4.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$18$ |
not computed |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t + 6\right) x + 3 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + t^2$ |
undefined |
| 3.3.6.18a4.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x^{2} ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$6$ |
$18$ |
not computed |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t^{2} x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + t^2$ |
$[1, 4]$ |
| 3.3.6.18a5.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$18$ |
not computed |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 3\right) x + 3 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + (2 t^2 + t)$ |
undefined |
| 3.3.6.18a5.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 6 x\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$6$ |
$18$ |
not computed |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + (t^2 + 2 t)$ |
$[1, 4]$ |
| 3.3.6.18a6.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$6$ |
$18$ |
$C_3^3:\SOPlus(4,2)$ (as 18T339) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 3 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + (t^2 + 2 t + 2)$ |
$[1, 4]$ |
| 3.3.6.21a1.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^3:C_{18}$ (as 18T159) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x^{3} + \left(3 t^{2} + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.21a1.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 ( x^{3} + 2 x + 1 )^{3} + 3 x ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^3:C_6$ (as 18T85) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.21a1.3 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
$S_3 \times C_3$ (as 18T3) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$18$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
$[1, 5]$ |
| 3.3.6.21a1.4 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x^{2} ( x^{3} + 2 x + 1 )^{3} + 3 ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_9\times S_3$ (as 18T16) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$9$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t^{2} x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
$[1, 5]$ |
| 3.3.6.21a2.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 5]$ |
| 3.3.6.21a3.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x^{2} ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(6 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + t$ |
undefined |
| 3.3.6.21a3.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
$\He_3:D_6$ (as 18T125) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t x^{2} + 3$ |
$[2, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + t$ |
$[1, 5]$ |
| 3.3.6.21a4.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(6 t^{2} + 6 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + (t + 1)$ |
undefined |
| 3.3.6.21a5.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 x ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^3:C_{18}$ (as 18T159) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x^{3} + \left(6 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2 t$ |
$[1, 5]$ |
| 3.3.6.21a5.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 ( x^{3} + 2 x + 1 )^{3} + 6 x ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(6 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2 t$ |
$[1, 5]$ |
| 3.3.6.21a6.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^2:C_6$ (as 18T20) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + t^2$ |
undefined |
| 3.3.6.21a6.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x ( x^{3} + 2 x + 1 )^{3} + \left(3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^2:C_{18}$ (as 18T82) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x^{3} + 6 x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + t^2$ |
undefined |
| 3.3.6.21a6.3 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x^{2} ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x^{3} + \left(3 t^{2} + 3 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + t^2$ |
$[1, 5]$ |
| 3.3.6.21a6.4 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 ( x^{3} + 2 x + 1 )^{3} + 3 x^{2} ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^3:C_6$ (as 18T85) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t^{2} x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + t^2$ |
$[1, 5]$ |
| 3.3.6.21a7.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^3:C_{18}$ (as 18T159) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x^{3} + \left(3 t^{2} + 3 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + (t^2 + t + 1)$ |
undefined |
| 3.3.6.21a7.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 x ( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 6 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + (t^2 + t + 1)$ |
undefined |
| 3.3.6.21a8.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^2:D_6$ (as 18T42) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(6 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + (t^2 + t + 2)$ |
undefined |
| 3.3.6.21a9.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(6 x^{2} + 3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$S_3 \times C_3$ (as 18T3) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$18$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(6 t^{2} + 3 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + (t^2 + 2 t)$ |
undefined |
| 3.3.6.21a9.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 ( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_9\times S_3$ (as 18T16) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$9$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x^{3} + \left(6 t^{2} + 3 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + (t^2 + 2 t)$ |
undefined |
| 3.3.6.21a9.3 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 6 x\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + (t^2 + 2 t)$ |
$[1, 5]$ |
| 3.3.6.21a9.4 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 ( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x^{3} + \left(3 t^{2} + 6 t\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + (t^2 + 2 t)$ |
$[1, 5]$ |
| 3.3.6.21a10.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^2:D_6$ (as 18T42) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 3 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + (t^2 + 2 t + 2)$ |
$[1, 5]$ |
| 3.3.6.21a11.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x + 3\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^3:C_6$ (as 18T85) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(6 t^{2} + 3 t\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + (2 t^2 + 2)$ |
undefined |
| 3.3.6.21a11.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x^{2} ( x^{3} + 2 x + 1 )^{3} + \left(3 x + 3\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^3:C_{18}$ (as 18T159) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 x^{3} + 6 t^{2} x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + (2 t^2 + 2)$ |
undefined |
| 3.3.6.21a11.3 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(6 x^{2} + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t x^{3} + \left(6 t^{2} + 6 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + (2 t^2 + 2)$ |
$[1, 5]$ |
| 3.3.6.21a11.4 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x ( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
$C_3^2:C_6$ (as 18T20) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(6 t^{2} + 3 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + (2 t^2 + 2)$ |
$[1, 5]$ |
| 3.3.6.21a12.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 6 x + 3\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
$S_3 \times C_6$ (as 18T6) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 6 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + (2 t^2 + t)$ |
undefined |
| 3.3.6.21a12.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(6 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
$\He_3:D_6$ (as 18T125) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(6 t^{2} + 3 t\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + (2 t^2 + t)$ |
$[1, 5]$ |
| 3.3.6.21a13.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 3 x + 3\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$21$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 3 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + (2 t^2 + t + 2)$ |
undefined |
| 3.3.6.21a13.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(6 x^{2} + 3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$6$ |
$21$ |
$\He_3:D_6$ (as 18T125) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + (2 t^2 + t + 2)$ |
$[1, 5]$ |
| 3.3.6.27a1.1 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 x ( x^{3} + 2 x + 1 )^{4} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$27$ |
not computed |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t + 6\right) x^{5} + \left(6 t^{2} + 6 t + 3\right) x^{4} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.27a1.2 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 x ( x^{3} + 2 x + 1 )^{4} + 3 ( x^{3} + 2 x + 1 ) + 3 x + 9$ |
$3$ |
$3$ |
$6$ |
$27$ |
$C_3\wr C_6$ (as 18T453) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t + 6\right) x^{5} + \left(6 t^{2} + 6 t + 3\right) x^{4} + 12 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.27a1.3 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 x ( x^{3} + 2 x + 1 )^{4} + 3 ( x^{3} + 2 x + 1 ) + 3 x + 18$ |
$3$ |
$3$ |
$6$ |
$27$ |
not computed |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t + 6\right) x^{5} + \left(6 t^{2} + 6 t + 3\right) x^{4} + 21 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.27a1.4 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x^{2} ( x^{3} + 2 x + 1 )^{5} + 6 x ( x^{3} + 2 x + 1 )^{4} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$27$ |
not computed |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 6 t + 6\right) x^{5} + \left(6 t^{2} + 6 t + 3\right) x^{4} + 21 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.27a1.5 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x^{2} ( x^{3} + 2 x + 1 )^{5} + 6 x ( x^{3} + 2 x + 1 )^{4} + 3 ( x^{3} + 2 x + 1 ) + 3 x + 9$ |
$3$ |
$3$ |
$6$ |
$27$ |
$C_3\wr C_6$ (as 18T453) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t x^{5} + 6 t x^{4} + 3 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.27a1.6 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 x^{2} ( x^{3} + 2 x + 1 )^{5} + 6 x ( x^{3} + 2 x + 1 )^{4} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$27$ |
not computed |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 3 t\right) x^{5} + 6 t x^{4} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.27a1.7 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x ( x^{3} + 2 x + 1 )^{5} + 6 x ( x^{3} + 2 x + 1 )^{4} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$27$ |
$C_3\wr C_6$ (as 18T453) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t^{2} x^{5} + 3 t^{2} x^{4} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.27a1.8 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 3 x ( x^{3} + 2 x + 1 )^{5} + 6 x ( x^{3} + 2 x + 1 )^{4} + 3 ( x^{3} + 2 x + 1 ) + 3 x + 9$ |
$3$ |
$3$ |
$6$ |
$27$ |
$C_3\wr C_6$ (as 18T453) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + \left(3 t^{2} + 3\right) x^{5} + \left(6 t^{2} + 6 t + 3\right) x^{4} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.27a1.9 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 )^{5} + 6 x ( x^{3} + 2 x + 1 )^{4} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$27$ |
$C_3\wr C_6$ (as 18T453) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t x^{5} + 6 t x^{4} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.3.6.27a1.10 |
$18$ |
$( x^{3} + 2 x + 1 )^{6} + 6 x ( x^{3} + 2 x + 1 )^{5} + 6 x ( x^{3} + 2 x + 1 )^{4} + 3 ( x^{3} + 2 x + 1 ) + 3 x$ |
$3$ |
$3$ |
$6$ |
$27$ |
not computed |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{6} + 3 t^{2} x^{5} + 6 t x^{4} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
